A public mathematical database of Conservative Matrix Fields — path-independent matrix recurrences connecting continued fractions, pFq hypergeometric series, and named constants such as ζ(3), π, ln(2) and ζ(5).
The CMF Atlas is currently in its beta stage. This platform is designed to facilitate mathematical research by making Conservative Matrix Fields (CMF) more accessible to the global community. We are actively verifying existing CMFs in the database and searching for new high dimensional CMFs.
The cubic symmetric CMF whose walk limit is ζ(3). Foundational to Apéry's irrationality proof.
View entry →Hypergeometric CMFs from RamanujanTools — 3F2, 4F3, 5F4, 6F5 families targeting ζ(3), ζ(5), π, Catalan.
Browse pFq CMFs →Walk any CMF with explicit f(x,y) up to depth 2000 using 30-digit mpmath precision. Compare against known constants from the registry.
Open Explorer →Cite CMF Atlas
Vesterlund, D. (2026). CMF Atlas: A Database of Conservative Matrix Fields. https://davidvesterlund.com/cmf-atlas/